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dir="ltr"><section class="mf-section-0" id="mf-section-0"><style data-mw-deduplicate="TemplateStyles:r1238436933">.mw-parser-output .ombox{margin:4px 0;border-collapse:collapse;border:1px solid #a2a9b1;background-color:var(--background-color-neutral-subtle,#f8f9fa);box-sizing:border-box;color:var(--color-base,#202122)}.mw-parser-output .ombox.mbox-small{font-size:88%;line-height:1.25em}.mw-parser-output .ombox-speedy{border:2px solid #b32424;background-color:#fee7e6}.mw-parser-output .ombox-delete{border:2px solid #b32424}.mw-parser-output .ombox-content{border:1px solid #f28500}.mw-parser-output .ombox-style{border:1px solid #fc3}.mw-parser-output .ombox-move{border:1px solid #9932cc}.mw-parser-output .ombox-protection{border:2px solid #a2a9b1}.mw-parser-output .ombox .mbox-text{border:none;padding:0.25em 0.9em;width:100%}.mw-parser-output .ombox .mbox-image{border:none;padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .ombox .mbox-imageright{border:none;padding:2px 0.9em 2px 0;text-align:center}.mw-parser-output .ombox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ombox .mbox-invalid-type{text-align:center}@media(min-width:720px){.mw-parser-output .ombox{margin:4px 10%}.mw-parser-output .ombox.mbox-small{clear:right;float:right;margin:4px 0 4px 1em;width:238px}}body.skin--responsive .mw-parser-output table.ombox img{max-width:none!important}@media screen{html.skin-theme-clientpref-night .mw-parser-output .ombox-speedy{background-color:#310402}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .ombox-speedy{background-color:#310402}}</style><table class="plainlinks ombox ombox-notice" role="presentation"><tbody><tr><td class="mbox-image"><span typeof="mw:File"><span><img alt="Blue tick" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/eb/Blue_check.svg/30px-Blue_check.svg.png" decoding="async" width="30" height="30" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/eb/Blue_check.svg/45px-Blue_check.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/eb/Blue_check.svg/60px-Blue_check.svg.png 2x" data-file-width="600" data-file-height="600"></span></span></td><td class="mbox-text"><b>This page documents an English Wikipedia <a href="/wiki/Category:Wikipedia_content_guidelines" title="Category:Wikipedia content guidelines">content guideline</a>.</b><br><div style="font-size: 90%;">Editors should generally follow it, though <a href="/wiki/Wikipedia:Ignore_all_rules" title="Wikipedia:Ignore all rules">exceptions</a> may apply. Substantive edits to this page should reflect <a href="/wiki/Wikipedia:PGCHANGE" class="mw-redirect" title="Wikipedia:PGCHANGE">consensus</a>. When in doubt, discuss first on <a href="/wiki/Wikipedia_talk:Scientific_citation_guidelines" title="Wikipedia talk:Scientific citation guidelines">this guideline's talk page</a>.</div></td><td class="mbox-imageright"><style data-mw-deduplicate="TemplateStyles:r1252059228">.mw-parser-output .module-shortcutboxplain{float:right;margin:0 0 0 1em;border:1px solid var(--border-color-base,#a2a9b1);background-color:var(--background-color-base,#fff);padding:0.3em 0.6em 0.2em 0.6em;text-align:center;font-size:85%}.mw-parser-output .module-shortcutboxleft{float:left;margin:0 1em 0 0}.mw-parser-output .module-shortcutlist{display:inline-block;border-bottom:1px solid var(--border-color-base,#a2a9b1);margin-bottom:0.2em}.mw-parser-output .module-shortcutboxplain ul{font-weight:bold}.mw-parser-output .module-shortcutanchordiv{position:relative;top:-3em}.mw-parser-output li .module-shortcutanchordiv{float:right}.mw-parser-output .mbox-imageright .module-shortcutboxplain{padding:0.4em 1em 0.4em 1em;line-height:1.3;margin:0}</style><div class="module-shortcutanchordiv"><span id="WP:SCG"></span><span id="WP:SCICITE"></span></div><div class="module-shortcutboxplain noprint" role="note"><div class="module-shortcutlist"><a href="/wiki/Wikipedia:Shortcut" title="Wikipedia:Shortcut">Shortcuts</a></div><style data-mw-deduplicate="TemplateStyles:r1126788409">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style><div class="plainlist"><ul><li><span class="plainlinks"><a class="external text" href="https://en.wikipedia.org/w/index.php?title=Wikipedia:SCG&redirect=no">WP:SCG</a></span></li><li><span class="plainlinks"><a class="external text" href="https://en.wikipedia.org/w/index.php?title=Wikipedia:SCICITE&redirect=no">WP:SCICITE</a></span></li></ul></div></div></td></tr></tbody></table> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">This page is a <a href="/wiki/Wikipedia:Policies_and_guidelines" title="Wikipedia:Policies and guidelines">guideline</a> for <a href="/wiki/Wikipedia:WikiProject_Mathematics" title="Wikipedia:WikiProject Mathematics">Mathematics</a>, <a href="/wiki/Wikipedia:WikiProject_Physics" title="Wikipedia:WikiProject Physics">Physics</a>, <a href="/wiki/Wikipedia:WikiProject_Molecular_and_Cellular_Biology" class="mw-redirect" title="Wikipedia:WikiProject Molecular and Cellular Biology">Molecular and cellular biology</a> and <a href="/wiki/Wikipedia:WikiProject_Chemistry" title="Wikipedia:WikiProject Chemistry">Chemistry</a>. It expresses the consensus recommendations of editors in those projects about specific details of inline citation. Editors in other scientific projects should follow the practice followed by those projects.</div> <p>The <i><a href="/wiki/Wikipedia:No_original_research" title="Wikipedia:No original research">no original research</a></i> and <i><a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">verifiability</a></i> policies are of paramount importance to Wikipedia. <a href="/wiki/Wikipedia:Citing_sources#Inline_citations" title="Wikipedia:Citing sources">Inline citations</a>, which link specific reliable sources with specific pieces of information in the article, provide practical support for these policies by making it easier to check the article content. </p><p>This page applies the advice in the policies, and in the <a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources">citing sources guideline</a>, to referencing science and mathematics articles. The goal is to achieve a reasonable balance between ease of verification, readability and editability. This page also describes some sensible guidelines for dealing with issues that are specific to writing Wikipedia articles (compared to writing for the academic press). </p><p><a href="/wiki/Wikipedia:Footnotes" class="mw-redirect" title="Wikipedia:Footnotes">Footnotes</a> (<ref> tags) are used in examples throughout this page. <a href="/wiki/Wikipedia:Parenthetical_referencing" class="mw-redirect" title="Wikipedia:Parenthetical referencing">Parenthetical referencing</a> was a different type of referencing used on Wikipedia until September 2020, when a <a href="/wiki/Special:PermanentLink/976895063#Deprecate_parenthetical_citations" title="Special:PermanentLink/976895063">community discussion</a> reached a consensus to <a href="/wiki/Deprecation" title="Deprecation">deprecate</a> parenthetical referencing. <a href="/wiki/Wikipedia:CITEVAR" class="mw-redirect" title="Wikipedia:CITEVAR">Do not change any article's established citation style without discussing it first.</a> </p> <div id="toc" class="toc" role="navigation" aria-labelledby="mw-toc-heading"><input type="checkbox" role="button" id="toctogglecheckbox" class="toctogglecheckbox" style="display:none"><div class="toctitle" lang="en" dir="ltr"><h2 id="mw-toc-heading">Contents</h2><span class="toctogglespan"><label class="toctogglelabel" for="toctogglecheckbox"></label></span></div> <ul> <li class="toclevel-1 tocsection-1"><a href="#Uncontroversial_knowledge"><span class="tocnumber">1</span> <span class="toctext">Uncontroversial knowledge</span></a></li> <li class="toclevel-1 tocsection-2"><a href="#Articles_without_in-line_references"><span class="tocnumber">2</span> <span class="toctext">Articles without in-line references</span></a></li> <li class="toclevel-1 tocsection-3"><a href="#Citation_format"><span class="tocnumber">3</span> <span class="toctext">Citation format</span></a></li> <li class="toclevel-1 tocsection-4"><a href="#Examples,_derivations,_and_restatements"><span class="tocnumber">4</span> <span class="toctext">Examples, derivations, and restatements</span></a></li> <li class="toclevel-1 tocsection-5"><a href="#Attribution"><span class="tocnumber">5</span> <span class="toctext">Attribution</span></a></li> <li class="toclevel-1 tocsection-6"><a href="#See_also"><span class="tocnumber">6</span> <span class="toctext">See also</span></a></li> <li class="toclevel-1 tocsection-7"><a href="#Notes"><span class="tocnumber">7</span> <span class="toctext">Notes</span></a></li> <li class="toclevel-1 tocsection-8"><a href="#References"><span class="tocnumber">8</span> <span class="toctext">References</span></a></li> </ul> </div> </section><div class="mw-heading mw-heading2 ext-discussiontools-init-section section-heading" onclick="mfTempOpenSection(1)"><span class="indicator mf-icon mf-icon-expand mf-icon--small"></span><h2 id="Uncontroversial_knowledge" data-mw-thread-id="h-Uncontroversial_knowledge"><span data-mw-comment-start="" id="h-Uncontroversial_knowledge"></span>Uncontroversial knowledge<span data-mw-comment-end="h-Uncontroversial_knowledge"></span></h2><span class="mw-editsection"> <a role="button" href="/w/index.php?title=Wikipedia:Scientific_citation_guidelines&action=edit&section=1" title="Edit section: Uncontroversial knowledge" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>edit</span> </a> </span> </div><section class="mf-section-1 collapsible-block" id="mf-section-1"> <p>Some statements are uncontroversial and widely known among people familiar with a discipline. Such facts may be taught in university courses, found in textbooks, or contained in multiple references in the research literature (most importantly in review articles). Some examples are: </p> <ul><li><i><a href="/wiki/Special_relativity" title="Special relativity">Special relativity</a> combines <a href="/wiki/Galilean_relativity" class="mw-redirect" title="Galilean relativity">Galilean relativity</a> with the postulate that all observers will always measure the <a href="/wiki/Speed_of_light" title="Speed of light">speed of light</a> to be the same no matter what their state of uniform linear motion is.</i></li> <li><i>A frustrated <a href="/wiki/Spin_glass" title="Spin glass">spin glass</a> may have a large <a href="/wiki/Ground_state" title="Ground state">ground state</a> degeneracy.</i></li> <li><i><a href="/wiki/T-duality" title="T-duality">T-duality</a> relates <a href="/wiki/Type_IIA_string" class="mw-redirect" title="Type IIA string">type IIA</a> <a href="/wiki/String_theory" title="String theory">superstring theory</a> to <a href="/wiki/Type_IIB_string" class="mw-redirect" title="Type IIB string">type IIB</a> superstring theory.</i></li></ul> <p>These statements are not common knowledge, but the first should be known to anyone with an undergraduate background in physics, the second to anyone knowledgeable about <a href="/wiki/Condensed_matter_physics" title="Condensed matter physics">condensed matter physics</a>, and the third to anyone knowledgeable about string theory. </p><p>The verifiability criteria require that such statements be sourced so that in principle anyone can verify them. However, in many articles it is cumbersome to provide an in-line reference for every statement. In addition, such dense referencing can obscure the logical interdependence of statements. Therefore, in sections or articles that present well-known and uncontroversial information – information that is readily available in most common and obvious books on the subject – it is acceptable to give an inline citation for one or two authoritative sources (and possibly a more accessible source, if one is available) in such a way as to indicate that these sources can be checked to verify statements for which no other in-line citation is provided. These inline citations are often inserted either after the first sentence of a paragraph or after the last sentence of the paragraph; a single convention should be chosen for each article. </p><p>For example, from <a href="/wiki/Aldol_reaction" title="Aldol reaction">aldol reaction</a>: </p> <style data-mw-deduplicate="TemplateStyles:r1244412712">.mw-parser-output .templatequote{overflow:hidden;margin:1em 0;padding:0 32px}.mw-parser-output .templatequotecite{line-height:1.5em;text-align:left;margin-top:0}@media(min-width:500px){.mw-parser-output .templatequotecite{padding-left:1.6em}}</style><blockquote class="templatequote"><p>The <b>aldol reaction</b> is an important <a href="/wiki/Carbon-carbon_bond" class="mw-redirect" title="Carbon-carbon bond">carbon-carbon bond</a> forming <a href="/wiki/Organic_reaction" title="Organic reaction">reaction</a> in <a href="/wiki/Organic_chemistry" title="Organic chemistry">organic chemistry</a><sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> involving the addition of an <a href="/wiki/Enol" title="Enol">enol</a> or <a href="/wiki/Enolate" title="Enolate">enolate</a> anion to an <a href="/wiki/Aldehyde" title="Aldehyde">aldehyde</a> or <a href="/wiki/Ketone" title="Ketone">ketone</a>.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> In the <b>aldol addition</b>, the reaction results in a β-hydroxy <a href="/wiki/Ketone" title="Ketone">ketone</a> (or <a href="/wiki/Aldehyde" title="Aldehyde">aldehyde</a>), also called an "aldol" (<b>ald</b>ehyde + alcoh<b>ol</b>). In the <a href="/wiki/Aldol_condensation" title="Aldol condensation">aldol condensation</a>, the initial aldol adduct undergoes <a href="/wiki/Dehydration" title="Dehydration">dehydration</a> (loss of water) to form an <a href="/wiki/%CE%91,%CE%B2-unsaturated_carbonyl_compound" class="mw-redirect" title="Α,β-unsaturated carbonyl compound">α,β-unsaturated ketone</a> (or aldehyde). </p><p>The enol or enolate is itself generated from a <a href="/wiki/Carbonyl_compound" class="mw-redirect" title="Carbonyl compound">carbonyl compound</a>, often an aldehyde or ketone, using acid or base. If the enol or enolate is formed <a href="/wiki/In_situ" title="In situ">in situ</a>, the process can be considered as an acid or base-catalyzed reaction of one carbonyl compound with another. This may involve one aldehyde or ketone reacting with itself. Alternatively two <i>different</i> carbonyl compounds may be used, in which case the reaction is known as a <b>crossed aldol</b> reaction. In the scheme shown, the enol or enolate of a methyl ketone reacts with an aldehyde. </p> <style data-mw-deduplicate="TemplateStyles:r1236298596">.mw-parser-output .fake-heading{color:var(--color-emphasized,#000000);background:none;margin:0;overflow:hidden;padding-bottom:0.17em;page-break-after:avoid;padding-top:0.5em}.mw-parser-output .fake-heading.h1,.mw-parser-output .fake-heading.h2{border-bottom:1px solid var(--border-color-base,#a2a9b1);margin-bottom:0.25em;margin-top:1em;padding:0;font-family:"Linux Libertine","Georgia","Times","Source Serif Pro",serif;line-height:1.375}body.skin-monobook .mw-parser-output .fake-heading.h1,body.skin-monobook .mw-parser-output .fake-heading.h2{font-family:inherit;line-height:inherit}body.skin-timeless .mw-parser-output .fake-heading.h1,body.skin-timeless .mw-parser-output .fake-heading.h2{border-bottom:3px solid #c8ccd1}.mw-parser-output .fake-heading.h1{font-size:1.8em}body.skin-timeless .mw-parser-output .fake-heading.h1{font-size:2em}.mw-parser-output .fake-heading.h2{font-size:1.5em}body.skin-timeless .mw-parser-output .fake-heading.h2{font-size:1.8em}.mw-parser-output .fake-heading.h3,.mw-parser-output .fake-heading.h4,.mw-parser-output .fake-heading.h5,.mw-parser-output .fake-heading.h6{font-weight:bold;margin-top:0.3em;margin-bottom:0;padding-bottom:0;line-height:1.6}.mw-parser-output .fake-heading.h3{font-size:1.2em}.mw-parser-output .fake-heading.h4{font-size:100%}</style><div class="fake-heading h3">References</div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text">Wade, L. G. <i>Organic Chemistry</i>, 6th ed., Prentice Hall, Upper Saddle River, New Jersey, 2006; pp. 1056–1066. <style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/013187151X" title="Special:BookSources/013187151X">013187151X</a></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text">Smith, M. B.; March, J. <i>Advanced Organic Chemistry</i>, 5th ed., Wiley Interscience, New York, 2001; pp. 1218–1223. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-471-58589-0" title="Special:BookSources/0-471-58589-0">0-471-58589-0</a></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text">Mahrwald, R. (ed.) <i>Modern Aldol Reactions, Volumes 1 and 2</i>, Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, Germany, 2004. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/3-527-30714-1" title="Special:BookSources/3-527-30714-1">3-527-30714-1</a>.</span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><a href="/wiki/Clayton_Heathcock" title="Clayton Heathcock">Heathcock, C. H.</a> (1991), "The aldol reaction", in <i>Comprehensive Organic Synthesis</i>, B. M. Trost and I. Fleming (Eds.), Pergamon Press, Oxford, 1991; vol. 2, pp. 133–179. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0080405932" title="Special:BookSources/0080405932">0080405932</a>. (Review)</span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text">Mukaiyama, T., "The directed aldol reaction", in <i>Organic Reactions</i>, William G. Dauben, et al (eds.) John Wiley & Sons, New York, 1982; vol. 28, pp. 203–331. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0471861413" title="Special:BookSources/0471861413">0471861413</a>. (Review)</span> </li> </ol></div></div> </blockquote> <p>Five references are provided early on: two textbooks, a specialized monograph on aldol reactions, and two review articles. Most readers would assume that the bulk of the statements in the comparatively short Wikipedia article could be verified by checking any of these references, and so it may only be necessary to provide additional in-line references for controversial statements, for recent discoveries that are not covered in the standard references, for historical and academic attribution, and for verifying more specialized statements or subsections. </p><p>When quoting widely known numbers such as the <a href="/wiki/Speed_of_light" title="Speed of light">speed of light</a> or numbers published by the <a href="/wiki/Particle_Data_Group" title="Particle Data Group">Particle Data Group</a> or in the <a href="/wiki/CRC_Press" title="CRC Press">CRC Handbook of Chemistry and Physics</a>, a reference might only be needed in the most relevant article. Wikipedia policy <a href="/wiki/Wikipedia:V" class="mw-redirect" title="Wikipedia:V">WP:V</a> states that if an editor requests that a particular statement be sourced, that request should be fulfilled. In this case, it may be advisable to add an in-line citation if this would prevent future confusion. However, if the statement is easily found in the principal references already given in the article, a citation may instead be provided on the article's talk page. </p> </section><div class="mw-heading mw-heading2 ext-discussiontools-init-section section-heading" onclick="mfTempOpenSection(2)"><span class="indicator mf-icon mf-icon-expand mf-icon--small"></span><h2 id="Articles_without_in-line_references" data-mw-thread-id="h-Articles_without_in-line_references"><span data-mw-comment-start="" id="h-Articles_without_in-line_references"></span>Articles without in-line references<span data-mw-comment-end="h-Articles_without_in-line_references"></span></h2><span class="mw-editsection"> <a role="button" href="/w/index.php?title=Wikipedia:Scientific_citation_guidelines&action=edit&section=2" title="Edit section: Articles without in-line references" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>edit</span> </a> </span> </div><section class="mf-section-2 collapsible-block" id="mf-section-2"> <p>Sometimes, short articles (including many stubs) provide a list of references without any inline citations. This can satisfy the sourcing policies when the entire contents of the article can be verified from the sources listed. An example of a very short article covered by <a href="/wiki/Wikipedia:General_references" class="mw-redirect" title="Wikipedia:General references">general references</a> is provided by the linked revision of "<a href="/wiki/Special:PermanentLink/398125410" title="Special:PermanentLink/398125410">low basis theorem</a>". </p><p>As an article matures to include more than a few sentences, inline citations are added to make it clear which material in the article can be verified by which source. If a few general references cover the bulk of an article, consider using the technique described in <a href="#Uncontroversial_knowledge">§ Uncontroversial knowledge</a> above. This can be done regardless of article length. </p><p>Some material, including direct quotations, contentious material about living people, and any material whose verifiability has been challenged, should always be accompanied by an inline citation, regardless of the length of the article. For more information on these special cases, see <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">Wikipedia:Verifiability</a> and <a href="/wiki/Wikipedia:Biographies_of_living_people" class="mw-redirect" title="Wikipedia:Biographies of living people">Wikipedia:Biographies of living people</a>. </p> </section><div class="mw-heading mw-heading2 ext-discussiontools-init-section section-heading" onclick="mfTempOpenSection(3)"><span class="indicator mf-icon mf-icon-expand mf-icon--small"></span><h2 id="Citation_format" data-mw-thread-id="h-Citation_format"><span data-mw-comment-start="" id="h-Citation_format"></span>Citation format<span data-mw-comment-end="h-Citation_format"></span></h2><span class="mw-editsection"> <a role="button" href="/w/index.php?title=Wikipedia:Scientific_citation_guidelines&action=edit&section=3" title="Edit section: Citation format" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>edit</span> </a> </span> </div><section class="mf-section-3 collapsible-block" id="mf-section-3"> <p>Since Wikipedia <a href="/wiki/Wikipedia:NOT#Wikipedia_is_not_a_paper_encyclopedia" class="mw-redirect" title="Wikipedia:NOT">is not a paper encyclopedia</a>, references do not need to be as concise as they are in journals. In particular, it may be helpful to give the title of a journal article, and to give the complete name of the journal (<i><a href="/wiki/Astrophysical_Journal" class="mw-redirect" title="Astrophysical Journal">Astrophysical Journal</a></i> instead of <i>Ap. J.</i>). It is important to provide linkage data such as the <a href="/wiki/ISBN" title="ISBN">ISBN</a> for books, and relevant database identifiers that link to papers or their bibliographic records. Such linkages facilitate the <a href="/wiki/Wikipedia:V" class="mw-redirect" title="Wikipedia:V">verification</a> of sourced statements. Examples include the <a href="/wiki/Digital_object_identifier" title="Digital object identifier">DOI</a> for articles in many areas of science, the <a href="/wiki/PMID" class="mw-redirect" title="PMID">PMID</a> for articles in medicine and the <a href="/wiki/Mathematical_Reviews" title="Mathematical Reviews">MR</a> number for mathematics articles. For physics and mathematics, many articles are available as <a href="/wiki/Preprint" title="Preprint">preprints</a> on the <a href="/wiki/ArXiv" title="ArXiv">arXiv</a>, so it is helpful to provide the preprint number and a <a href="/wiki/URL" title="URL">URL</a>. For articles published before 1992, and many others, there is no arXiv preprint. Instead, consider linking to the <a href="/wiki/Astrophysics_Data_System" title="Astrophysics Data System">ADS</a>, <a href="/wiki/SPIRES" class="mw-redirect" title="SPIRES">SPIRES</a> or <a href="/wiki/MathSciNet" title="MathSciNet">MathSciNet</a> entry, if one is available, or directly to the entry at the journal's website. The <span class="nowrap">{{</span><a href="/wiki/Template:Bibcode" title="Template:Bibcode">bibcode</a><span class="nowrap">}}</span>, <span class="nowrap">{{</span><a href="/wiki/Template:Arxiv" title="Template:Arxiv">arxiv</a><span class="nowrap">}}</span> and <span class="nowrap">{{</span><a href="/wiki/Template:MathSciNet" class="mw-redirect" title="Template:MathSciNet">MathSciNet</a><span class="nowrap">}}</span> templates may prove useful for creating these database links in free-form citations, or such links can be automatically generated when using the <code>{{<a href="/wiki/Template:Citation" title="Template:Citation">citation</a>}}</code>, <code>{{<a href="/wiki/Template:Cite_book" title="Template:Cite book">cite book</a>}}</code> or <code>{{<a href="/wiki/Template:Cite_journal" title="Template:Cite journal">cite journal</a>}}</code> templates using the corresponding parameters. </p><p>For some topics the bibliography available may address different audiences, e.g. undergraduate vs. graduate, or levels or rigor, e.g. statistics textbooks for social scientists vs. those addressed to mathematicians. When the audience of a text in the further reading section is not self-evident, it may be useful to annotate it as discussed at <a href="/wiki/Wikipedia:FURTHER" class="mw-redirect" title="Wikipedia:FURTHER">WP:FURTHER</a>. </p> </section><div class="mw-heading mw-heading2 ext-discussiontools-init-section section-heading" onclick="mfTempOpenSection(4)"><span class="indicator mf-icon mf-icon-expand mf-icon--small"></span><h2 id="Examples,_derivations,_and_restatements" data-mw-thread-id="h-Examples,_derivations,_and_restatements"><span id="Examples.2C_derivations.2C_and_restatements"></span><span data-mw-comment-start="" id="h-Examples,_derivations,_and_restatements"></span>Examples, derivations, and restatements<span data-mw-comment-end="h-Examples,_derivations,_and_restatements"></span></h2><span class="mw-editsection"> <a role="button" href="/w/index.php?title=Wikipedia:Scientific_citation_guidelines&action=edit&section=4" title="Edit section: Examples, derivations, and restatements" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>edit</span> </a> </span> </div><section class="mf-section-4 collapsible-block" id="mf-section-4"> <p>Wikipedia is neither a textbook nor a journal. Nonetheless, in mathematics and the mathematical sciences, it is frequently helpful to quote theorems, include simple derivations, and provide illustrative examples. For reasons of notation, clarity, consistency, or simplicity it is often necessary to state things in a slightly different way than they are stated in the references, to provide a different derivation, or to provide an example. This is standard practice in journals, and does not make any claim of novelty.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> In Wikipedia articles this does not constitute <a href="/wiki/Wikipedia:NOR" class="mw-redirect" title="Wikipedia:NOR">original research</a> and is perfectly permissible – in fact, encouraged – provided that anyone who reads and understands the references can easily see how the material in the Wikipedia article can be inferred. Furthermore, copying extensively from a source with only minor modifications is not normally permitted by <a href="/wiki/Wikipedia:COPYRIGHT" class="mw-redirect" title="Wikipedia:COPYRIGHT">copyright</a> law, unless the source has a free license. </p><p>Wikipedia's no-original-research policy allows <a href="/wiki/Wikipedia:Routine_calculations" class="mw-redirect" title="Wikipedia:Routine calculations">routine calculations</a> based on data from reliable sources. Routine calculations frequently involve converting units, rounding to appropriate levels of <a href="/wiki/Precision_and_accuracy" class="mw-redirect" title="Precision and accuracy">precision</a> for the article, describing quantitative relationships in words, and other simple methods that both accurately describe the information from the source(s) and do not tend to advance a novel argument. As an example, the article on the <a href="/wiki/Lambda-CDM_model" title="Lambda-CDM model">Lambda-CDM model</a> quotes values for Hubble parameter <i>h</i> and the fraction of the present universe made up of <a href="/wiki/Baryon" title="Baryon">baryons</a>, <i>Ω</i><sub>b</sub>. For technical reasons having to do with their <a href="/wiki/Fisher_matrix" class="mw-redirect" title="Fisher matrix">Fisher matrix</a>, the <a href="/wiki/WMAP" class="mw-redirect" title="WMAP">WMAP</a> collaboration quotes values for <i>h</i> and <i>Ω</i><sub>b</sub><i>h</i><sup>2</sup>.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> The values quoted in the article are more useful for non-experts. Anyone who looks at the WMAP paper, and has a basic knowledge of error analyses, will understand how to go from one to the other. </p><p>If a calculation, although routine, takes more than one or two steps, it may be helpful to present the details of the calculation in a note to the text. For an example, see the detailed calculation in the article on <a href="/wiki/Methane_clathrate" title="Methane clathrate">Methane clathrate</a> giving a derivation of the statement in the article's lead that one liter of methane clathrate solid at STP contains, on average, 168 liters of methane gas. </p> </section><div class="mw-heading mw-heading2 ext-discussiontools-init-section section-heading" onclick="mfTempOpenSection(5)"><span class="indicator mf-icon mf-icon-expand mf-icon--small"></span><h2 id="Attribution" data-mw-thread-id="h-Attribution"><span data-mw-comment-start="" id="h-Attribution"></span>Attribution<span data-mw-comment-end="h-Attribution"></span></h2><span class="mw-editsection"> <a role="button" href="/w/index.php?title=Wikipedia:Scientific_citation_guidelines&action=edit&section=5" title="Edit section: Attribution" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>edit</span> </a> </span> </div><section class="mf-section-5 collapsible-block" id="mf-section-5"> <p>Wikipedia's <a href="/wiki/Wikipedia:No_original_research" title="Wikipedia:No original research">no original research</a> policy requires that we make it clear assertions do not originate with Wikipedia's editors. This is achieved by providing sources for the material in Wikipedia articles. It is also important, however, for our articles to clearly indicate the person who first discovered an astronomical object, first proved a theorem, first performed an experiment, or was otherwise responsible for the idea being discussed. The process of giving credit to the original discoverer will be called attribution here. </p><p>Articles should provide attribution for experiments, theorems, astronomical objects, and similar topics, when the original discoverer is known. Many editors prefer to supply the original source for an idea when providing this attribution, for example: </p> <ul><li><i><a href="/wiki/Supernova_1987A" class="mw-redirect" title="Supernova 1987A">Supernova 1987A</a> was discovered by <a href="/wiki/Ian_Shelton" title="Ian Shelton">Ian Shelton</a> and Oscar Duhalde at the <a href="/wiki/Las_Campanas_Observatory" title="Las Campanas Observatory">Las Campanas Observatory</a> in <a href="/wiki/Chile" title="Chile">Chile</a> on February 24, 1987, and independently by Albert Jones in <a href="/wiki/New_Zealand" title="New Zealand">New Zealand</a>.</i><sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup></li> <li><i>Kervaire and Milnor showed that the <a href="/wiki/Orientability" title="Orientability">oriented</a> 7-sphere has 28 different smooth structures (or 15 ignoring orientations), and in higher dimensions there are usually many different smooth structures on a sphere.</i><sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> (from <a href="/wiki/Poincar%C3%A9_conjecture" title="Poincaré conjecture">Poincaré conjecture</a>)</li></ul> <p>When the original reference is not suitable as an introduction to the idea, either because it is outdated or because it contains serious errors, it is helpful to note this in an annotation: </p> <ul><li><i>Beginning with observations in 1912, <a href="/wiki/Vesto_Slipher" title="Vesto Slipher">Vesto Slipher</a> discovered that most <a href="/wiki/Spiral_nebula" class="mw-redirect" title="Spiral nebula">spiral nebulae</a> had considerable <a href="/wiki/Redshift" title="Redshift">redshifts</a>.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup></i></li></ul> <p>Numerical data can also be attributed to the person or group that obtained it. For example, from the <a href="/wiki/Neutrino" title="Neutrino">neutrino</a> article: </p> <dl><dd><i>The strongest upper limit on the masses of neutrinos comes from <a href="/wiki/Physical_cosmology" title="Physical cosmology">cosmology</a>: careful analysis of cosmological data, such as the cosmic microwave background radiation, <a href="/wiki/Galaxy_survey" class="mw-redirect" title="Galaxy survey">galaxy surveys</a> and the <a href="/wiki/Lyman-alpha_forest" title="Lyman-alpha forest">Lyman-alpha forest</a> indicate that the sum of the neutrino masses must be less than 0.3 <a href="/wiki/Electron_volt" class="mw-redirect" title="Electron volt">electron volts</a>.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup></i></dd></dl> <p>This provides attribution for academic and historical purposes, and also makes it clear how readers can understand where a number comes from. This not only makes Wikipedia a more convenient resource for readers, but makes it easier to update when better data become available. </p><p>A related issue is the attribution of <a href="/wiki/Eponym" title="Eponym">eponyms</a> (terms derived from people's names) such as: </p> <ul><li><i>...the Michelson–Morley experiment<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup>...</i></li> <li><i>...the Sunyaev–Zel'dovich effect<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup>...</i></li> <li><i>...the Green–Schwarz anomaly cancellation mechanism<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup>...</i></li> <li><i>...the αβγ neutron capture theory<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup>...</i></li> <li><i>...the Kaluza–Klein theory of dimensional reduction<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup>...</i></li></ul> <p>If Wikipedia has an article about an eponymous topic – such as <a href="/wiki/Michelson%E2%80%93Morley_experiment" title="Michelson–Morley experiment">Michelson–Morley experiment</a>, <a href="/wiki/Sunyaev%E2%80%93Zel%27dovich_effect" class="mw-redirect" title="Sunyaev–Zel'dovich effect">Sunyaev–Zel'dovich effect</a>, <a href="/wiki/Green%E2%80%93Schwarz_mechanism" title="Green–Schwarz mechanism">Green–Schwarz mechanism</a>, <a href="/wiki/Alpher%E2%80%93Bethe%E2%80%93Gamow_paper" title="Alpher–Bethe–Gamow paper">Alpher–Bethe–Gamow paper</a> and <a href="/wiki/Kaluza%E2%80%93Klein_theory" title="Kaluza–Klein theory">Kaluza–Klein theory</a> – then editors of this article should, if feasible, explain why the names are attached to the result or experiment. To this end, editors of these articles should consider researching and citing the original papers, even if those papers were not originally used as sources in writing the article. However, articles that only link to an eponymous article might not cite the original papers, depending on context. In this case, a reader looking for a reference may easily click the article link to find it. </p> </section><div class="mw-heading mw-heading2 ext-discussiontools-init-section section-heading" onclick="mfTempOpenSection(6)"><span class="indicator mf-icon mf-icon-expand mf-icon--small"></span><h2 id="See_also" data-mw-thread-id="h-See_also"><span data-mw-comment-start="" id="h-See_also"></span>See also<span data-mw-comment-end="h-See_also"></span></h2><span class="mw-editsection"> <a role="button" href="/w/index.php?title=Wikipedia:Scientific_citation_guidelines&action=edit&section=6" title="Edit section: See also" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>edit</span> </a> </span> </div><section class="mf-section-6 collapsible-block" id="mf-section-6"> <ul><li><a href="/wiki/Wikipedia:Manual_of_Style_(mathematics)" class="mw-redirect" title="Wikipedia:Manual of Style (mathematics)">Wikipedia:Manual of Style (mathematics)</a></li> <li><a href="/wiki/Wikipedia:Manual_of_Style_(Medicine-related_articles)" class="mw-redirect" title="Wikipedia:Manual of Style (Medicine-related articles)">Wikipedia:Manual of Style (Medicine-related articles)</a></li> <li><a href="/wiki/Wikipedia:WikiProject_Chemicals/Style_guidelines" title="Wikipedia:WikiProject Chemicals/Style guidelines">Wikipedia:WikiProject Chemicals/Style guidelines</a> (very out of date on citations!)</li> <li><a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources">Wikipedia:Citing sources</a></li> <li><a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">Wikipedia:Verifiability</a></li> <li><a href="/wiki/Wikipedia:No_original_research" title="Wikipedia:No original research">Wikipedia:No original research</a></li> <li><a href="/wiki/Wikipedia:Citation_templates" title="Wikipedia:Citation templates">Wikipedia:Citation templates</a></li> <li><a href="/wiki/Wikipedia:Manual_of_Style_(summary_style)#References,_citations_and_external_links" class="mw-redirect" title="Wikipedia:Manual of Style (summary style)">Wikipedia:Manual of Style (summary style)#References, citations and external links</a></li> <li><a href="/wiki/WebCite" title="WebCite">WebCite</a> – tool to archive webpages to allow stable citation links.</li></ul> </section><div class="mw-heading mw-heading2 ext-discussiontools-init-section section-heading" onclick="mfTempOpenSection(7)"><span class="indicator mf-icon mf-icon-expand mf-icon--small"></span><h2 id="Notes" data-mw-thread-id="h-Notes"><span data-mw-comment-start="" id="h-Notes"></span>Notes<span data-mw-comment-end="h-Notes"></span></h2><span class="mw-editsection"> <a role="button" href="/w/index.php?title=Wikipedia:Scientific_citation_guidelines&action=edit&section=7" title="Edit section: Notes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>edit</span> </a> </span> </div><section class="mf-section-7 collapsible-block" id="mf-section-7"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239543626"><div class="reflist reflist-columns references-column-width reflist-columns-2"> <ol class="references"> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text">See <a href="/wiki/Manifold_Destiny" title="Manifold Destiny">Manifold Destiny</a> for a possible counterexample.</span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFD._N._Spergel2013" class="citation web cs1">D. N. Spergel; et al. (WMAP collaboration) (2013). <a rel="nofollow" class="external text" href="https://lambda.gsfc.nasa.gov/product/map/current/map_bibliography.cfm">"Bibliography of WMAP Science Team Publications"</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Bibliography+of+WMAP+Science+Team+Publications&rft.date=2013&rft.au=D.+N.+Spergel&rft_id=http%3A%2F%2Flambda.gsfc.nasa.gov%2Fproduct%2Fmap%2Fcurrent%2Fmap_bibliography.cfm&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWikipedia%3AScientific+citation+guidelines" class="Z3988"></span></span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMarsden1987" class="citation journal cs1">Marsden, B. G. (24 February 1987). <a rel="nofollow" class="external text" href="http://www.cbat.eps.harvard.edu/iauc/04300/04316.html">"Nova Centauri 1986"</a>. <i><a href="/wiki/IAU_Circular" title="IAU Circular">IAU Circular</a></i>. <b>4316</b> (2): 2. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1987IAUC.4316....2M">1987IAUC.4316....2M</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=IAU+Circular&rft.atitle=Nova+Centauri+1986&rft.volume=4316&rft.issue=2&rft.pages=2&rft.date=1987-02-24&rft_id=info%3Abibcode%2F1987IAUC.4316....2M&rft.aulast=Marsden&rft.aufirst=B.+G.&rft_id=http%3A%2F%2Fwww.cbat.eps.harvard.edu%2Fiauc%2F04300%2F04316.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWikipedia%3AScientific+citation+guidelines" class="Z3988"></span></span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKervaireMilnor1963" class="citation journal cs1">Kervaire, Michel A.; Milnor, John W. (1963). "Groups of Homotopy Spheres: I". <i><a href="/wiki/Annals_of_Mathematics" title="Annals of Mathematics">Annals of Mathematics</a></i>. 2nd Series. <b>77</b> (3): 504–537. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2307%2F1970128">10.2307/1970128</a>. <a href="/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/1970128">1970128</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Annals+of+Mathematics&rft.atitle=Groups+of+Homotopy+Spheres%3A+I&rft.volume=77&rft.issue=3&rft.pages=504-537&rft.date=1963&rft_id=info%3Adoi%2F10.2307%2F1970128&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F1970128%23id-name%3DJSTOR&rft.aulast=Kervaire&rft.aufirst=Michel+A.&rft.au=Milnor%2C+John+W.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWikipedia%3AScientific+citation+guidelines" class="Z3988"></span>. This paper calculates the structure of the group of smooth structures on an <i>n-</i>sphere for <i>n</i> > 4.</span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text">Slipher first reports on his measurement in the inaugural volume of the <i><a href="/wiki/Lowell_Observatory_Bulletin" class="mw-redirect" title="Lowell Observatory Bulletin">Lowell Observatory Bulletin</a></i>, pp.2.56–2.57 <a rel="nofollow" class="external autonumber" href="http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1913LowOB...1b..56S&db_key=AST&data_type=HTML&format=&high=448f04e38822894">[1]</a>. His article entitled "The radial velocity of the Andromeda Nebula" reports making the first Doppler measurement on September 17, 1912. In his report Slipher writes: "The magnitude of this velocity, which is the greatest hitherto observed, raises the question whether the velocity-like displacement might not be due to some other cause, but I believe we have at present no other interpretation for it." Three years later, in the journal <i><a href="/wiki/Popular_Astronomy_(US_magazine)" title="Popular Astronomy (US magazine)">Popular Astronomy</a></i>, Vol. 23, pp. 21–24 <a rel="nofollow" class="external autonumber" href="http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1915PA.....23...21S&db_key=AST&data_type=HTML&format=&high=448f04e38822894">[2]</a>, Slipher wrote a review entitled "Spectrographic Observations of Nebulae". In it he states, "The early discovery that the great Andromeda spiral had the quite exceptional velocity of −300 km(/s) showed the means then available, capable of investigating not only the spectra of the spirals but their velocities as well." Slipher reported the velocities for 15 spiral nebulae spread across the entire <a href="/wiki/Celestial_sphere" title="Celestial sphere">celestial sphere</a>, all but three having observable "positive" (that is recessional) velocities.</span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGoobarHannestadMörtsellTu2006" class="citation journal cs1">Goobar, A.; Hannestad, S.; Mörtsell, E.; Tu, H. (2006). "A new bound on the neutrino mass from the SDSS baryon acoustic peak". <i><a href="/wiki/Journal_of_Cosmology_and_Astroparticle_Physics" title="Journal of Cosmology and Astroparticle Physics">Journal of Cosmology and Astroparticle Physics</a></i>. <b>6</b> (6): 19. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/astro-ph/0602155">astro-ph/0602155</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2006JCAP...06..019G">2006JCAP...06..019G</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1088%2F1475-7516%2F2006%2F06%2F019">10.1088/1475-7516/2006/06/019</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:119535760">119535760</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Cosmology+and+Astroparticle+Physics&rft.atitle=A+new+bound+on+the+neutrino+mass+from+the+SDSS+baryon+acoustic+peak&rft.volume=6&rft.issue=6&rft.pages=19&rft.date=2006&rft_id=info%3Aarxiv%2Fastro-ph%2F0602155&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A119535760%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1088%2F1475-7516%2F2006%2F06%2F019&rft_id=info%3Abibcode%2F2006JCAP...06..019G&rft.aulast=Goobar&rft.aufirst=A.&rft.au=Hannestad%2C+S.&rft.au=M%C3%B6rtsell%2C+E.&rft.au=Tu%2C+H.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWikipedia%3AScientific+citation+guidelines" class="Z3988"></span></span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMichelsonMorley1887" class="citation journal cs1">Michelson, A. A.; Morley, E. W. (1887). <a rel="nofollow" class="external text" href="http://www.biodiversitylibrary.org/item/121645#page/463/mode/1up">"On the relative motion of the earth and the luminiferous æther"</a>. <i>The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science</i>. 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"Cosmic microwave background anisotropies". <i><a href="/wiki/Annual_Review_of_Astronomy_and_Astrophysics" title="Annual Review of Astronomy and Astrophysics">Annual Review of Astronomy and Astrophysics</a></i>. <b>40</b>: 171–216. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/astro-ph/0110414">astro-ph/0110414</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2002ARA&A..40..171H">2002ARA&A..40..171H</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1146%2Fannurev.astro.40.060401.093926">10.1146/annurev.astro.40.060401.093926</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:569887">569887</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Annual+Review+of+Astronomy+and+Astrophysics&rft.atitle=Cosmic+microwave+background+anisotropies&rft.volume=40&rft.pages=171-216&rft.date=2002&rft_id=info%3Aarxiv%2Fastro-ph%2F0110414&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A569887%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1146%2Fannurev.astro.40.060401.093926&rft_id=info%3Abibcode%2F2002ARA%26A..40..171H&rft.aulast=Hu&rft.aufirst=Wayne&rft.au=Dodelson%2C+Scott&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWikipedia%3AScientific+citation+guidelines" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKolbTurner1988" class="citation book cs1">Kolb, Edward; 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